Ch.7 - Quantum MechanicsWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Solution: The quantum-mechanical treatment of the hydrogen atom gives this expression for the wave function, ψ, of the 1s orbital:where r is the distance from the nucleus and a0 is 52.92 pm. The probability of

Problem

The quantum-mechanical treatment of the hydrogen atom gives this expression for the wave function, ψ, of the 1s orbital:

where r is the distance from the nucleus and a0 is 52.92 pm. The probability of finding the electron in a tiny volume at distance r from the nucleus is proportional to ψ2. The total probability of finding the electron at all points at distance r from the nucleus is proportional to 4πr2ψ2. Calculate the values (to three significant figures) of ψ, ψ2, and 4πr2ψ2 to fill in the following table and sketch a plot of each set of values versus r. Compare the latter two plots with those in the figure below.